Algebra Refresher for Adults
Rebuild algebra from scratch in seven days, from reading expressions to solving linear and quadratic equations with confidence.
This course is for members
$9 unlocks every course in the library, this one included, plus a credit to build a topic of your own and at least 10 new courses every month.
What you will learn about Algebra Refresher for Adults
The 7-day sprint
- Reading Algebra as a Language. A letter is a number you do not know yet, and the equal sign says that the two sides name the very same number.
- The Arithmetic Algebra Runs On. Order of operations, signed numbers, and the distributive property decide what you are allowed to do to an expression.
- Solving Linear Equations. You solve an equation by doing the same thing to both sides until the variable stands alone, which keeps the two sides equal at every step.
- Turning Words Into Equations. Most real problems become solvable the moment you name the unknown and write one sentence of math that is true about it.
- Lines, Slope, and Graphs. A linear relationship changes by the same amount for every one unit of input, and that steady rate is the slope of its line.
- Exponents, Polynomials, and Factoring. Multiplying expressions out and factoring them back up are the same distributive property run in opposite directions.
- Quadratics and Choosing a Method. A quadratic equation usually has two solutions, and knowing three ways to find them lets you pick the fastest route for the problem in front of you.
The 80/20: the 7 concepts that matter most
- The equal sign is a relationship, not an instruction
- A variable is a number you have not identified yet
- Inverse operations, applied to both sides
- The distributive property in both directions
- See the structure before you compute
- Linear relationships and constant rate of change
- Keep more than one strategy, and always check
The core idea, explained like you are 5
An equation is a claim that two expressions name the exact same number, so anything you do to one side you must do to the other, and solving means finding which values make the claim true.
Then the quiz and the ladder
10 questions that correct you when you are wrong, and beginner, intermediate, advanced levels, each with a practical exercise.
Created Sep 13, 2026. 1 mistake reported by learners, 0 addressed in a rebuild, the rest pending.
Written from these sources
- High School: Algebra » Seeing Structure in Expressions | Common Core State Standards Initiative, thecorestandards.org. day 1 structure of expressions and the 80/20 structure concept.
- High School: Algebra | Common Core State Standards Initiative, thecorestandards.org. the `p + 0.05p` framing and algebraic conventions.
- Common Core High School Algebra: Seeing Structure in Expressions, ct4me.net. factoring to reveal zeros, day 6 and day 7.
- College and Career Readiness Standards for Adult Education, lincs.ed.gov. scope of adult-level algebra standards across the sprint.
- College and Career Readiness: Resource Guide for the ..., careeronestop.org. rationale for a short, just-in-time adult refresher.
- Mathematics Proficiency Guide for Teachers of Adult Basic Education, doe.mass.edu. balancing concepts, fluency, and application in the sprint.
- Elementary Algebra, oalib-perpustakaan.upi.edu. the seven-day topic sequence.
- Index - Elementary Algebra 2e | OpenStax, openstax.org. placement of vocabulary such as variables on both sides.
- Practice Guide iconPractice Guide, ies.ed.gov. structure and alternative strategies, days 6 and 7.
- Teaching Strategies for Improving Algebra Knowledge in ..., ies.ed.gov. strategy comparison recommendation in the 80/20 section.
- 1 WHAT WORKS CLEARINGHOUSETM U.S. DEPARTMENT OF EDUCATION, ies.ed.gov. the 15 percent tip example on day 2.
- Evidence-Based Practices for Teaching Strategies for ..., education.vermont.gov. language that reflects mathematical structure.
- Algebraic thinking in the early grades, files.eric.ed.gov. operational versus relational views of the equal sign.
- Students' Early Grade Understanding of the Equal Sign ..., files.eric.ed.gov. the `4 + 3 = box + 5` error pattern on day 1.
- A Further Investigation to Introducing the Equal Sign in China, files.eric.ed.gov. why variables on both sides trips learners up.
- Keys to the Gate? Equal Sign Knowledge at Second Grade Predicts Fourth-Grade Algebra Competence - PMC, pmc.ncbi.nlm.nih.gov. relational equal sign as sameness and interchangeability.
- WHAT DOES RESEARCH SUGGEST ABOUT TEACHING AND LEARNING THE EQUAL SIGN?, cambridgemaths.org. reading the equal sign as is the same as.
- Louisiana State University Louisiana State University LSU Scholarly Repository, repository.lsu.edu. equality as a relation, ELI5 expert stage.
- Assessment Guide for Educators: Mathematical Reasoning, ged.com. percent, unit rate, and rate targets on day 4.
- Mathematical Reasoning - GED, ged.com. no-calculator portion, mental fraction and decimal work.